1. Field of the Invention (Technical Field)
The present invention relates to the art of teaching apparatus, and more particularly to a teaching apparatus for demonstration and experimentation with respect to moments of inertia and how they affect the spin axis, with application for use as a demonstration in mechanics classes and in mechanics experiments.
2. Background Art
Note that the following discussion refers to a number of publications by author(s) and year of publication, and that due to recent publication dates certain publications are not to be considered as prior art vis-a-vis the present invention. Discussion of such publications herein is given for more complete background and is not to be construed as an admission that such publications are prior art for patentability determination purposes.
The free rotator is almost always discussed in college-level intermediate and advanced mechanics classes. The object of this discussion is to understand moments of inertia and how they affect the spin axis. The theory for the behavior of the axis of rotation is covered in physics textbooks, but a clear physical display of the phenomenon is lacking. The usual demonstration is to throw a box, a tennis racket, a hammer, a book, or similar objects in the air and observe the resulting rotation. Two references showing this procedure are found in Physics Teacher. John B. Hart: Great ellipsoids of inertia and space physics, Phys Teach 6:118-122 (1968); Allan Waistad: The hammer flip, Phys Teach 28:556-7 (1990). However, using an object such as the foregoing only allows a transient observation lasting about 1 second. In addition, generally speaking only the beginning and end conditions can be observed adequately. No meaningful experimentation can be conducted using objects such as the foregoing, given the difficulty of observation and measurement.
While many physics texts cover the theory of the free rotator, there has heretofore been no commercially available demonstrators of the free rotator. The reason for this is that most supports for the spinning rotator make it not truly free. William B. Case and Michael A. Shay: On the interesting behavior of a gimbal-mounted gyroscope, Am J Phys 60:503-6 (1992). A gyroscope made of a spherical ball floated in a hemispherical bowl using compressed air as the support mechanism has been described. Harold A. Daw: Two air supported devices for physics laboratories and for physics demonstrations, Am J Phys 33:322 (1965). The degree of interaction between the support and the rotating sphere is minimal. A number of uses have been made of the air supported bearing for gyroscopes. Robert G. Marclay: Air suspension gyroscope, Am J Phys 28:150 (1960); Bernard H. Duane: Air suspension gyroscope, Am J Phys 23:147 (1955); O. L. de Lange and J. Pierrus: Measurement of inertial and non inertial properties of an air suspension gyroscope, Am J Phys Vol. 61 pp. 974-81 (1993); and William G. Harter and Chong C. Kim: Singular motions of asymmetric rotators, Am J Phys 44:1080-3 (1976). However, a gyroscope has, by definition, a net off balance and therefore a torque. For demonstration of the free rotator, and for certain experiments, both symmetric and asymmetric rotators are desired, and additionally the degree of asymmetry should be variable for many demonstrations and experiments.
Certain balls, such as bowling balls, have been described with asymmetric weighting. See, for example, U.S. Pat. Nos. 4,523,757, 5,058,901 and 5,437,579. However, these are designed to be thrown or rolled, generally have weighting on the spin axis, have finger holes, cannot be used as symmetric rotators, are not marked to indicate the axis, and are not used with an air support film. Other prior art describes air support of balls, particularly of low-density balls, but does not disclose use of an air support film, which is essentially frictionless, as opposed to an air jet, and similarly does not teach uses with free rotators. See, for example, U.S. Pat. Nos. 2,074,363, 4,858,921, 5,011,144 and 5,314,368.
The invention provides a free rotator apparatus, which apparatus includes a substantially homogeneous solid sphere with one or more cylindrical holes along a diameter of the sphere, a cylindrical insert of different density from the sphere disposed within each cylindrical hole, and a concave air support with curvature substantially matching that of the sphere. In this apparatus, there may be a single cylindrical hole traversing the diameter of the sphere, in which case the apparatus may be a symmetric rotator. In the apparatus, there may also be four cylindrical holes, each of a depth less than the radius of the sphere, with two holes lying along a first diameter and the remaining two holes lying along a second diameter at right angles to the first diameter. The apparatus with four cylindrical holes may be a symmetric rotator, or if the inserts within the holes along the first diameter have a different weight than the inserts within the holes along the second diameter, may be an asymmetric rotator.
In a preferred embodiment of the apparatus, the exterior surface of the insert has the same radius of curvature as the exterior surface of the sphere. The insert can include a threaded screw along the axis of the hole and disposed opposite the exterior, and the interior of the hole can then terminate in a threaded cylinder, such that the threaded screw may be threadably engaged with the threaded cylinder. The insert can further include two or more indentations on the exterior surface whereby rotational torque may be applied to the insert by means of a suitable tool. In another embodiment, the insert further includes a threaded cylinder disposed within the exterior surface of the insert, whereby a screw may be threadably engaged with the threaded cylinder to facilitate removal of the insert from the cylindrical hole. The yet another embodiment, the insert may be retained within the cylindrical hole by friction.
The apparatus can further include a source of pressurized gas in connection with the concave air support. The pressurized gas can be compressed air. The concave air support can include one or more holes, most preferably at the base thereof, for entry of pressurized gas. In this apparatus, the sphere may rotate freely within the concave air support, and is supported within the concave air support on an air film, and preferably a thin air film. The apparatus may further be provided such that the instantaneous spin axis can be directly recorded on the surface of the sphere.
The invention also includes a method for demonstrating the path of the spin axis of a free rotator, including the steps of providing a substantially homogeneous solid sphere with one or more cylindrical holes along a diameter of the sphere and a cylindrical insert of different density from the sphere disposed within each cylindrical hole, providing a concave air support with curvature substantially matching that of the sphere and a source of pressurized gas, spinning the sphere within the concave air support, and at two or more spaced intervals marking the spin axis on the surface of the sphere.
A primary object of the present invention is to provide an apparatus and method for demonstrating and recording the path of the spin axis for both symmetric and asymmetric rotators.
Another object of the present invention is to provide a spherical rotator on an essentially frictionless air bed.
Yet another object of the present invention is to provide an asymmetric rotator wherein the degree of asymmetry may be adjusted.
Another advantage of the present invention is that it permits experimentations on asymmetric rotators, by altering the amount of asymmetry.
Yet another advantage of the present invention is that the rotators may be rotated about any axis, as there is no interference from the support.
Other objects, advantages and novel features, and further scope of applicability of the present invention will be set forth in part in the detailed description to follow, taken in conjunction with the accompanying drawings, and in part will become apparent to those skilled in the art upon examination of the following, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims.